Finite Group Databasebeta

← #14298613

Subgroups — #14298613

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#709C211yesmaximal, characteristic
2C3×#65421C211yesmaximal, characteristic
3#11748624C211yesmaximal, characteristic
4#11746378C211yesmaximal, characteristic, complemented
5C5×#4555C211yesmaximal, characteristic, complemented
6#11745976C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599530—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12#91815C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16Dic3×C22⋊D5—22no—
17Dic3×D20—21no—
18C4×D5×Dic3C412yescomplemented
19#91357C412yescomplemented
20Dic3×Dic10—21no—
21C3×#3956—21no—
22C3×#3955—21no—
23#90995—22no—
24#70131—51nomaximal, Hall
25C4×#709—31no—
26#65421D311yescharacteristic
27#65295—31no—
28C5×#339—31no—
29#64777—31no—
30#64751—31no—
31#64743—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×C5×Dic3—21no—
34C2×C3×C22⋊D5D412yes—
35C3×#709—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5C2×C412yes—
41C2×C3×Dic10D411yescharacteristic
42C2×D5×Dic3—22no—
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46#6719—21no—
47#6719—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4×Dic15—21no—
51C4×Dic15C2×C412yes—
52C5×#217—21no—
53C5×C4⋊Dic3—21no—
54C4×C5×Dic3—21no—
55C4×C5×Dic3—21no—
56C4×C5×Dic3C2×C411yescharacteristic
57C4×C5×Dic3C2×C411yescharacteristic
58C3×#681—21no—
59C3×#681—21no—
60C2×C3×#168—21no—
61#6668—22no—
62#6665—22no—
63Dic3×Dic5—22no—
64Dic3×#41—51no—
65C3×#413—51no—
66#5240—51no—
67#4557—51no—
68#4557—51no—
69#4555—51no—
70#4555D511yescharacteristic, complemented
71C2×#709C2×D311yescharacteristic
72C2×C5×M16C2×D311yescharacteristic
73C5×#117—31no—
74C2×C42×C5—31no—
75C4×C22⋊D5—62no—
76#4072—31no—
77#4072—31no—
78C2×#681C2×D311yescharacteristic
79C4×D20—61no—
80#4018—32no—
81C42×D5—32no—
82C4×Dic10—61no—
83#3956—21no—
84#3955—21no—
85#3938—62no—
86#1827—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5C22⋊C412yes—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×Dic15—22no—
96C2×Dic15—41no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—42no—
100C2×C5×Dic3—41no—
101C3×C22⋊D5—22no—
102C3×C22⋊D5—22no—
103C2×C3×Dic5C22⋊C412yes—
104C3×D20—21no—
105C3×D20—21no—
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×Dic10—21no—
109C3×Dic10—21no—
110D5×Dic3—44no—
111C3×C5×C8—41no—
112C3×#168—41no—
113C2×C3×#41—51no—
114C2×C3×M16—51no—
115C2×C3×M16C2×D511yescharacteristic
116Q8×Dic3—101no—
117D4×Dic3—101no—
118D4×Dic3—102no—
119#926—51no—
120#926—52no—
121#926—51no—
122#926C2×D511yescharacteristic
123C2×C4×Dic3—52no—
124C2×C4×Dic3C2×D511yescharacteristic
125C3×#101—101no—
126C3×#100—101no—
127#834—102no—
128C22×C4×C5—61no—
129C22×C4×C5C22×D311yescharacteristic
130C2×C22⋊D5D1212yes—
131#709—21no—
132#709—21no—
133#709—21no—
134#709—21no—
135C2×D20#6711yescharacteristic
136C2×C4×D5—62no—
137C2×C4×D5C4×D312yes—
138C2×Dic10#6711yescharacteristic
139C5×M16—21no—
140C5×M16—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—61no—
143C5×C22⋊C4—61no—
144C42×C5—31no—
145C42×C5—31no—
146C42×C5—61no—
147C42×C5—61no—
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150#685—62no—
151C4⋊Dic5—61no—
152C4⋊Dic5—61no—
153#683—62no—
154C4×Dic5—32no—
155C4×Dic5—62no—
156C4×Dic5—61no—
157#681—21no—
158#681—21no—
159C2×#168—21no—
160C4×#41—151no—
161#413—51no—
162#410—151no—
163#339—31no—
164#339—151no—
165H(3,ℤ/4)—151no—
166H(3,ℤ/4)—151no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#12311yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C2×C3×D5—22no—
172C2×C3×D5—42no—
173C3×C4×C5#11711yescharacteristic
174C3×C4×C5#11711yescharacteristic
175C3×C4×C5#12311yescharacteristic
176C3×C4×C5#12311yescharacteristic
177Dic15—42no—
178Dic15—81no—
179C3×Dic5—22no—
180C5×Dic3—22no—
181C5×Dic3—41no—
182C5×Dic3—81no—
183C3×#41—101no—
184C3×#41—101no—
185C3×#41—101no—
186C3×#41—101no—
187C2×C3×Q8—51no—
188C2×C3×D4—52no—
189C2×C3×D4—51no—
190C22×C3×C4—52no—
191C22×C3×C4C22×D511yescharacteristic
192C22×Dic3—21no—
193C22×Dic3—102no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—101no—
197C3×M16—101no—
198C2×C3×C8—21no—
199C2×C3×C8—101no—
200#217—21no—
201#217—102no—
202#217—101no—
203#217—101no—
204C4⋊Dic3—21no—
205C4⋊Dic3—102no—
206C4⋊Dic3—101no—
207C4⋊Dic3—101no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3—52no—
211C4×Dic3—102no—
212C4×Dic3—101no—
213C4×Dic3C4×D511yescharacteristic
214C4×Dic3C4×D511yescharacteristic
215C23×C5C2×D1211yescharacteristic
216C22×D5(C2×D3)⋊C412yes—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5—122no—
220C2×C4×C5—121no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C2×C4×C5#23711yescharacteristic
223C2×C4×C5#23711yescharacteristic
224C2×C4×C5#23711yescharacteristic
225C2×C4×C5#23711yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C22⋊D5—22no—
228C22⋊D5—22no—
229C2×Dic5—62no—
230C2×Dic5—121no—
231C2×Dic5(C2×D3)⋊C412yes—
232D20—21no—
233D20—21no—
234C4×D5—22no—
235C4×D5—22no—
236C4×D5—124no—
237Dic10—21no—
238Dic10—21no—
239C5×C8—41no—
240#168—41no—
241C2×#41—51no—
242C2×M16—51no—
243C2×M16D3×D511yescharacteristic
244C4×Q8—301no—
245C4×D4—301no—
246C4×D4—302no—
247#117—31no—
248#117—152no—
249#117—151no—
250#117—151no—
251C2×C42—31no—
252C2×C42—152no—
253#101—101no—
254#100—101no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#38111yescharacteristic
260C3×D5—42no—
261C23×C3—52no—
262C23×C3D4×D511yescharacteristic
263C3×Q8—101no—
264C3×Q8—101no—
265C3×D4—102no—
266C3×D4—102no—
267C3×D4—101no—
268C3×D4—101no—
269C2×C3×C4—52no—
270C2×C3×C4—102no—
271C2×C3×C4—102no—
272C2×C3×C4C2×C4×D511yescharacteristic
273C2×C3×C4#70911yescharacteristic
274C2×C3×C4#70911yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4#71111yescharacteristic
277C2×C3×C4#71311yescharacteristic
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—42no—
281C2×Dic3—41no—
282C2×Dic3—102no—
283C2×Dic3—204no—
284C2×Dic3—201no—
285C3×C8—41no—
286C3×C8—201no—
287C22×C5—41no—
288C22×C5#88611yescharacteristic
289C22×C5#88611yescharacteristic
290C22×C5C2×(C2×D3)⋊C411yescharacteristic
291C2×D5—22no—
292C2×D5—42no—
293C4×C5—62no—
294C4×C5—121no—
295C4×C5—241no—
296C4×C5#87711yescharacteristic
297C4×C5#87711yescharacteristic
298C4×C5#93511yescharacteristic
299C4×C5#93511yescharacteristic
300Dic5—22no—
301Dic5—122no—
302Dic5—241no—
303#41—101no—
304#41—101no—
305#41—101no—
306#41—101no—
307C2×Q8—51no—
308C2×D4—52no—
309C2×D4—51no—
310C22×C4—52no—
311C22×C4—61no—
312C22×C4—302no—
313C22×C4C2×D3×D511yescharacteristic
314M16—21no—
315M16—21no—
316M16—101no—
317M16—101no—
318C2×C8—21no—
319C2×C8—101no—
320C4⋊C4—61no—
321C4⋊C4—302no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C22⋊C4—61no—
325C22⋊C4—302no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—31no—
329C42—31no—
330C42—61no—
331C42—61no—
332C42—152no—
333C42—302no—
334C42—301no—
335C3×C5#182711yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3—102no—
338C22×C3—202no—
339C22×C3D5×C22⋊C411yescharacteristic
340C22×C3#402911yescharacteristic
341C22×C3#404011yescharacteristic
342C3×C4—102no—
343C3×C4#401811yescharacteristic
344C3×C4#402911yescharacteristic
345C3×C4#403811yescharacteristic
346C3×C4#404011yescharacteristic
347Dic3—22no—
348Dic3—41no—
349Dic3—81no—
350Dic3—202no—
351Dic3—401no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5#494311yescharacteristic
356D5—42no—
357C23—52no—
358C23D5×D1211yescharacteristic
359Q8—101no—
360Q8—101no—
361D4—102no—
362D4—102no—
363D4—101no—
364D4—101no—
365C2×C4—52no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—122no—
371C2×C4—121no—
372C2×C4—302no—
373C2×C4—604no—
374C2×C4—601no—
375C2×C4#676511yescharacteristic
376C2×C4#676611yescharacteristic
377C2×C4C4×D3×D511yescharacteristic
378C2×C4#677911yescharacteristic
379C2×C4#678011yescharacteristic
380C2×C4D5×#6711yescharacteristic
381C8—41no—
382C8—201no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—202no—
387C2×C3#6495311yescharacteristic
388C5#7013111yescharacteristic, complemented, Sylow
389C22—41no—
390C22—102no—
391C22—202no—
392C22#9141311yescharacteristic
393C22#9141411yescharacteristic
394C22D5×(C2×D3)⋊C411yescharacteristic
395C4—62no—
396C4—102no—
397C4—121no—
398C4—241no—
399C4—602no—
400C4—1201no—
401C4#9139311yescharacteristic
402C4#9139411yescharacteristic
403C4#9140711yescharacteristic
404C4#9154811yescharacteristic
405C3#1059953011yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—202no—
410C2#1174887111yescharacteristic
subgroupG/H
centerC4#91394
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#381
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1827
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11746378C2semidirect
5. C5×#4555C2semidirect
6. #11745976C2semidirect
7. #11745971C2semidirect
18. C4×D5×Dic3C4semidirect
19. #91357C4semidirect
70. #4555D5semidirect
335. C3×C5#1827semidirect
388. C5#70131semidirect
405. C3#10599530semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Dic3×#7092
C3×#654212
#117486242
#117463782
C5×#45552
#117459762
#117459712
#105995303
#701315